Main applet window General Help JavaView Help.

For details of the basic operation of the program see the Main Help page. Some special options specific to the calculation of algebraic surfaces is below. Example definitions plus some explanation are also below.

These parameters control the range over which the surface is calculated. *Its
best if unequal values are chosen for the ranges. Otherwise certain degeneracies
may occur which can lead to poorer results. *

These parameters control how detailed the resulting mesh will be. Each of
these must be a power of two. The box specified by the range is split into a
number of smaller boxes and points of the faces of these boxes will be found
together with any singularities lying in the middle of them. The **Coarse**
parameter specifies the number of smaller boxes, by default 8 along the x, y,
z directions, i.e. 512 boxes. The **Fine** parameter specifies the smallest
box size used to find a singularity. The **Face** specifies how accurately
each face of the box is subdivided and the **edge** parameter specifies how
accurately each edge is subdivided.

Generally you will just want to change the **Coarse** parameter.
If the singularities are not calculated very well then you could also increase
the **Fine** parameter.
Lowering the other parameters may give quicker results. Not much will be gained
by increasing them. As a rule you should keep
**Coarse < Fine < Face < Edge** or the results will be unpredictable.

If a degenerate surface is specified the program can take a very long time to run. To prevent this from happening the cgi program will timeout after a certain time. This may mean the surface will not be calculated properly. If you want to calculate more complicated surfaces please email me at rich@singsurf.org and I'll provide a version you can run at home which does not have the timeout restriction.

Below are various examples of implicit surfaces, further examples can be found in the Algebraic Surface help page, but better results will be produced for polynomial function if the Algebraic Surface project is used instead. All the examples (except the super-ellipse) come from The Scientific Graphics Project.

**Sum of Sins**sin(x) + sin(y) + sin(z) = 0;

**super-ellipse**(abs((A - x)/a)^(2/e) + (abs(B - y)/b)^(2/e))^(e/f) + (abs(C - z)/c)^(2/f) = 1; A = 0.0; B = 0.0; C = 0.0; a = 0.75429300; b = 0.75429300; c = 2.07894000; e = 0.38533800; f = 0.09582500;

A generalisation of an ellipse. Set**timeout**to 100 and**Course**to 16 to get a good image.

**P (Schwarz P)**-
cos(x) + cos(y) + cos(z) = 0;

**D (Diamond)**-
sin(x) sin(y) sin(z) + sin(x) * cos(y) * cos(z) + cos(x) * sin(y) * cos(z) + cos(x) * cos(y) * sin(z) = 0;

**G (Gyroid)**-
cos(x) * sin(y) + cos(y) * sin(z) + cos(z) * sin(x) = 0;

**N (Neovius)**-
3*(cos(x) + cos(y) + cos(z)) + 4* cos(x) * cos(y) * cos(z) = 0.0;

**W (iWP)**-
cos(x) * cos(y) + cos(y) * cos(z) + cos(z) * cos(x) - cos(x) * cos(y) * cos(z) = 0;

**P_W (P W Hybrid)**-
4*(cos(x) * cos(y) + cos(y) * cos(z) + cos(z) * cos(x)) - 3* cos(x) * cos(y) * cos(z) = -2.4;

Web page, applet and Algebraic Surface program by Richard Morris

home page Email rich@singsurf.org. Copyright Jan 2001.